IndisputableMonolith.Cosmology.Cosmology
Module packaging Recognition Science cosmology primitives: a domain cost functional on scale factors, its nonnegativity, a positive canonical threshold, and an EOSDeep4 certificate bundle. Cosmologists working in the RS ladder cite it for the cost-of-expansion interface. Structure is mostly definitions plus elementary positivity lemmas over the imported J-cost.
claimDefines a cosmology domain cost $C_{\mathrm{dom}}$ (built from the RS $J$-cost), proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, introduces a positive canonical threshold $\theta_{\mathrm{can}}>0$, and packages an EOSDeep4 certificate type with an inhabited witness.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. Cosmology here is cast as a domain cost on expansion data, not as a separate GR Lagrangian.
The module sits on Constants (RS time quantum $\tau_0=1$ tick) and Cost (the $J$-cost algebra). Sibling objects include domainCost, pointwise evaluation, nonnegativity, canonicalThreshold with positivity, and the EOSDeep4Cert / cert bundle used as a typed witness that deep equation-of-state constraints hold in RS units.
Local setting: bridge RS-native units ($c=1$, $\hbar=\varphi^{-5}$, etc.) into cosmological bookkeeping without re-deriving the forcing chain T0–T8.
proof idea
Definition-heavy module. Domain cost is assembled from the imported $J$-cost; domainCost_at_eq is an evaluation identity; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity arguments. The certificate side (EOSDeep4Cert, cert, cert_inhabited) is a structure-plus-inhabitation pattern rather than a deep derivation.
why it matters in Recognition Science
Supplies the cosmology-facing cost and threshold interface so later RS cosmology results can quote a single domain cost and a canonical cutoff instead of rebuilding $J$ each time. No downstream edges are recorded in the graph yet; the module is an entry point under the Cosmology domain. It does not itself close forcing-chain steps T5–T8, but keeps cosmological claims inside the same $J$-cost and $\varphi$-ladder language as the rest of the monolith.
scope and limits
- Does not derive FLRW metrics or Einstein equations from RS axioms.
- Does not fix numerical cosmological parameters beyond the threshold interface.
- Does not prove late-time acceleration or dark-energy microphysics.
- Does not discharge forcing-chain landmarks T5–T8 inside this file.
- Does not claim observational fits; only cost/threshold/certificate scaffolding.